A seashell like a Moebius strip

The border of a Moebius strip consists of only one circumpherence: this animation shows what happens to the Moebius strip if we move this circumpherence in order to position it in the three-dimensional space in the usual way. The most natural way to do that produces as a result the so-called "crossed hood": instead, this animation leads to a seashell surface and during the process the Moebius strip never shows any self-intersection. Some buttons give you the possibility of cutting the Moebius strip (as we can see in the figure) and seeing it transparent, in order to visualize its structure.